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How many integers greater than 999 but not greater than 4000 can be formed, using the digits 0, 1, 2, 3, 4 if repetition of digits is allowed?

How many integers greater than 999 but not greater than 4000 can be formed, using the digits 0, 1, 2, 3, 4 if repetition of digits is allowed? Correct Answer 376

Calculation:

The smallest number in the series of 4-digit numbers is 1000.

 

The largest number in the series is 4000, the only 4-digit number to start with 4. 

 

The left-most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

 

The next 3 digits (hundreds, tens, and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

 

Hence, there are 3 x 5 x 5 x 5 = 375 numbers from 1000 to 3999.

 

Including 4000, the numbers will be 375 + 1 = 376.

 

∴ The number of integers is 376

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